Please refer to FIG. 1, which is the block diagram showing a discrete-time baseband equivalent model of the orthogonal frequency division multiplexing (OFDM) system 10 in the prior art. The orthogonal frequency division multiplexing system 10 includes a transmitter 12, a transmission channel 13 and a receiver 14. The transmitter 12 receives a transmitter input signal I1, and generates a transmitted time-domain signal S21 in response to the transmitter input signal I1. The transmitted time-domain signal S21 is referred to in this invention also as a frequency division multiplexing signal or a frequency division multiplexing time-domain signal. The transmitter 12 includes a signal generator 121 and a processing unit 122. The processing unit 122 includes an inverse discrete Fourier transforming (IDFT) unit 122RT and a cyclic prefix (CP) adding unit 122A. The receiver 14 includes a signal detecting unit 141 and a processing unit 142. The processing unit 142 includes a cyclic prefix (CP) removing unit 142D and a discrete Fourier transforming (DFT) unit 142T. The processing unit 122 is coupled to the signal generator 121 and generates the transmitted time-domain signal S21 in response to the transmitter input signal I1. The transmission channel 13 outputs a received time-domain signal S22 in response to transmitted time-domain signal S21. The received time-domain signal S22 is also referred to in this invention as a frequency division multiplexing signal or a frequency division multiplexing time-domain signal. The receiver 14 receives the received time-domain signal S22, and generates a receiver output signal O1. The processing unit 142 is coupled to the transmission channel 13, receives the received time-domain signal S22, and generates a receiver frequency-domain signal S3 in response to the received time-domain signal S22.
The transmitter input signal I1 is input to the transmitter 12, and the transmitter frequency-domain signal S1 of the frequency division multiplexing property is generated from passing the transmitter input signal I1 through the signal generator 121. The transmitted time-domain signal S21 is generated by passing the transmitter frequency-domain signal S1 through the inverse discrete Fourier transforming (IDFT) unit 122RT and the cyclic prefix (CP) adding unit 122A successively. The received time-domain signal S22 is obtained by passing the transmitted time-domain signal S21 through the transmission channel 13. The received time-domain signal S22 is input to the receiver 14. The receiver frequency-domain signal S3 is generated by passing the received time-domain signal S22 of the frequency division multiplexing property by the cyclic prefix (CP) removing unit 142D and the discrete Fourier transforming (DFT) unit 142T successively. The receiver frequency-domain signal S3 is sent to the signal detecting unit 141 for signal processing. The receiver frequency-domain signal S3 includes three components: a main signal S4, a residual intercarrier interference (ICI) S5 and a channel noise S6. The receiver frequency-domain signal S3 is detected by the signal detecting unit 141 using a signal detection method. The signal detection method can employ the methods of least squares, minimum mean square error, iterative minimum mean square error, decision feedback equalization, and maximum likelihood sequence estimation (MLSE).
For instance, carrier frequency shift and channel time-variation can result in ICI and degradation of the signal transmission performance in an orthogonal frequency division multiplexing (OFDM) communication system. The problem becomes especially serious when the carrier frequency is very high or when the user terminal moves at a fast speed. The problem can be understood by observing the mathematical relationship concerning the transmitter and the receiver in an OFDM system.
Let N be the size of the discrete Fourier transform (DFT) in the system. Then the relation between the transmitted signal and the received signal in an OFDM symbol interval can be expressed as in the following equation (1):y=Hx+w  (1)
wherein x is the N-vector of the transmitter signal samples in the frequency domain (S1), y is the N-vector of the receiver signal samples in the frequency domain (S3), H is the N×N channel matrix in the frequency domain, and w is the N-vector of the noise samples in the frequency domain (S6).
The channel matrix H is a diagonal matrix when there is no ICI. When there is ICI, non-zero values may appear not only along the diagonal but also in other locations of the matrix. This condition causes difficulty in detection of ODFM signals.
Theoretically, the best signal detector should consider all ICI terms. However, due to complexity and robustness concerns, usually only the main terms in the channel matrix H will be compensated. Since the main terms usually appear around the diagonal of the channel matrix H, a band structure shows up in the channel matrix H.
Please refer to the paper by Won Gi Jeon, Kyung Hi Chang and Yong Soo Cho, “An Equalization Technique for Orthogonal Frequency division Multiplexing Systems in Time-Varian Multipath Channels”, IEEE Transactions on Communications, Vol. 47, No. 1, pp. 27-32, January 1999. In this paper, normalized maximum Doppler frequencies on the order of 0.1 or less are considered, under which condition the channel variation over a short time period can be assumed to be linear, and a frequency-domain equalizer corresponding to the band structure of the channel matrix is proposed. In another paper by Philip Schniter, “Low-Complexity Equalization of OFDM in Doubly Selective Channels”, IEEE Transactions on Signal Processing, Vol. 52, No. 4, pp. 1002-1011, April 2004, normalized maximum Doppler frequencies up to the order of magnitude of 1 are considered, under which condition the ICI is more widely spread in the frequency domain, a time-domain window is recommended to partially cancel the effect of the channel time-variation and reduce the bandwidth of the channel matrix, and an iterative least squares error method is used to detect the signal. In the paper by Luca Rugini, Paolo Banelli and Geert Leus, “Simple Equalization of Time-Varying Channels for OFDM”, IEEE Communication Letters, Vol. 9, No. 7, pp. 619-621, July 2005, a block-type linear minimum mean square error equalizer is proposed to deal with the ICI, wherein the band channel matrix structure and triangular factorization of the channel autocorrelation matrix are used to reduce the equalizer complexity. In the paper by Shuichi Ohno, “Maximum Likelihood Inter-carrier Interference Suppression for Wireless OFDM with Null Subcarriers”, Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, March 2005, Vol. III, pp. 849-852, Viterbi MLSE in the frequency domain is used to deal with the ICI, and the band channel matrix structure is utilized to limit the algorithm complexity.
However, in these prior-art signal detection methods only a few main ICI terms are considered and the whole channel matrix H is approximated using these main ICI terms, which result in an irreducible floor in the bit error rate (BER) in a time-varying channel. On the other hand, if more ICI terms in the channel matrix are considered, then the transceiver complexity will increase. Therefore, a technology that can improve the signal transmission and reception performance of communication systems at a low complexity in needed.